Find an expression for the function whose graph is the line segment joining the points (2, -5) and (6, 9). (As?

Find an expression for the function whose graph is the line segment joining the points (2, -5) and (6, 9). (Assume that these points are in the form (x, f(x)).)

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The general equation for a line is
y= slope*x + yIntercept

First, find the slope of the line: it takes (6-2)= 4 units in the x direction to go (9-(-5))= 14 units in the y direction. The slope therefore is 14/4= 7/2

Now that we have the slope we need the yIntercept position ("where does the line cross the y-axis ?"). Solve the general equation above for yIntercept like so:
y= slope * x + yIntercept ----->
yIntercept= y - slope * x

Now use the slope value from above and any one of the points for x and y (it doesn't matter which point). This allows you to calculate the yIntercept. Put that yIntercept and the slope in the general equation and you are done.